Oscillation Theory for Neutral Differential Equations with Delay  book cover
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Oscillation Theory for Neutral Differential Equations with Delay



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ISBN 9780750301428
Published January 1, 1991 by CRC Press
288 Pages

 
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Book Description

With neutral differential equations, any lack of smoothness in initial conditions is not damped and so they have proven to be difficult to solve. Until now, there has been little information to help with this problem.

Oscillation Theory for Neutral Differential Equations with Delay fills a vacuum in qualitative theory of functional differential equations of neutral type. With much of the presented material previously unavailable outside Eastern Europe, this authoritative book provides a stimulus to research the oscillatory and asymptotic properties of these equations. It examines equations of first, second, and higher orders as well as the asymptotic behavior for tending toward infinity. These results are then generalized for partial differential equations of neutral type. The book also describes the historical development of the field and discusses applications in mathematical models of processes and phenomena in physics, electrical control and engineering, physical chemistry, and mathematical biology.

This book is an important tool not only for mathematicians, but also for specialists in many fields including physicists, engineers, and biologists. It may be used as a graduate-level textbook or as a reference book for a wide range of subjects, from radiophysics to electrical and control engineering to biological science.

Table of Contents

PREFACE
NOTATION

INTRODUCTION
Preliminary notes
Auxiliary assertions

FIRST ORDER NEUTRAL ORDINARY DIFFERENTIAL EQUATIONS
First order linear differential equations
First order differential equations with constant coefficients
First order differential equations with distributed delay
First order nonlinear differential equations
Oscillation and comparison of results in neutral differential equations and their applications to the delay logistic equation
Notes and comments to chapter 2

SECOND ORDER NEUTRAL ORDINARY DIFFERENTIAL EQUATIONS
Second order linear differential equations
Second order differential equations with constant coefficients
Second order differential equations with distributed delay
Second order nonlinear differential equations
Distribution of the zeros of the solutions of neutral differential equations
Notes and comments to chapter 3

NTH ORDER NEUTRAL ORDINARY DIFFERENTIAL EQUATIONS
nth order linear differential equations
nth order differential equations with constant coefficients
nth order nonlinear differential equations
Notes and comments to chapter 4

SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS OF NEUTRAL TYPE
Linear systems of ordinary differential equations with constant coefficients
Notes and comments to chapter 5

NEUTRAL PARTIAL DIFFERENTIAL EQUATIONS
Linear parabolic differential equations
Nonlinear parabolic differential equations
Parabolic differential equations with "maxima"
Linear hyperbolic differential equations
Nonlinear hyperbolic differential equations
Hyperbolic differential equations with "maxima"
Notes and comments to chapter 6

REFERENCES
INDEX

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